Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-06-29T05:48:20.427Z Has data issue: false hasContentIssue false
  • English
  • Français

Variance Reduction for Simulating Transient GI/G/1 Behavior

Published online by Cambridge University Press:  27 July 2009

Søren Asmussen  and
Chia-Li Wang
Søren Asmussen
Affiliation:
Department of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden
Chia-Li Wang
Affiliation:
Institute of Applied Mathematics, National Dong Hwa University, Hualien, Taiwan, ROC
Get access Rights & Permissions [Opens in a new window]

Abstract

A variety of methods for reducing the variance on Monte Carlo estimators of the expected waiting time Wn of the nth customer in a GI/G/1 queue are studied. The ideas involve Spitzer's identity, importance sampling, and sums with stratified or controlled randomized length.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 2 , April 1996 , pp. 197 - 205
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Abate, J. & Whitt, W. (1988). Transient behavior of regulated Brownian motion. Advances in Applied Probability 19: 560–598, 599–631.CrossRefGoogle Scholar
2.Asmussen, S. (1987). Applied probability and queues. Chichester: John Wiley & Sons.Google Scholar
3.Asmussen, S. (1990). Exponential families and regression in the Monte Carlo study of queues and random walks. Annals of Statistics 18: 1851–1867.CrossRefGoogle Scholar
4.Asmussen, S. (1992). Queueing simulation in heavy traffic. Mathematics of Operations Research 17: 84–111.CrossRefGoogle Scholar
5.Gaver, D.P. & Thompson, G.L. (1973). Programming and probability models in operations research. Monterey, CA: Brooks/Cole.Google Scholar
6.Glynn, P.W. (1983). Randomized estimators for time integrals. Technical Summary Report 2603, Mathematics Research Center, University of Wisconsin, Madison.Google Scholar
7.Glynn, P.W. & Iglehart, D.L. (1988). Simulation methods for queues. An overview. Queueing Systems 3: 221–255.CrossRefGoogle Scholar
8.Glynn, P.W. & Iglehart, D.L. (1989). Importance sampling in stochastic simulations. Management Science 35: 1367–1392.CrossRefGoogle Scholar
9.Minh, D.L. & Sorli, R.M. (1983). Simulating the GI/G/1 queue in heavy traffic. Operations Research 31: 966–971.CrossRefGoogle Scholar
10.Rubinstein, R.Y. (1981). Simulation and the Monte Carlo method. New York: Wiley.CrossRefGoogle Scholar
11.Whitt, W. (1989). Planning queueing simulations. Management Sciences 35: 1341–1366.CrossRefGoogle Scholar